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//! Probabilistic moments.

/// Compute an estimate of the population mean from a finite sample.
#[inline]
pub fn mean(data: &[f64]) -> f64 {
    data.iter().fold(0.0, |sum, &x| sum + x) / data.len() as f64
}

/// Compute an estimate of the population variance from a finite sample.
///
/// The estimate is unbiased. The computation is based on the
/// compensated-summation version of the [two-pass algorithm][1].
///
/// [1]: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Two-pass_algorithm
pub fn variance(data: &[f64]) -> f64 {
    let mu = mean(data);
    let n = data.len() as f64;
    let (mut sum1, mut sum2) = (0.0, 0.0);
    for &x in data {
        let delta = x - mu;
        sum1 = sum1 + delta * delta;
        sum2 = sum2 + delta;
    }
    (sum1 - sum2 * sum2 / n) / (n - 1.0)
}

#[cfg(test)]
mod tests {
    use assert;
    use moment;

    #[test]
    fn mean() {
        let data = [
             5.3766713954610001e-01,  1.8338850145950865e+00,
            -2.2588468610036481e+00,  8.6217332036812055e-01,
             3.1876523985898081e-01, -1.3076882963052734e+00,
            -4.3359202230568356e-01,  3.4262446653864992e-01,
             3.5783969397257605e+00,  2.7694370298848772e+00,
        ];
        assert::close(&[moment::mean(&data)], &[6.2428219709029698e-01], 1e-15);
    }

    #[test]
    fn variance() {
        let data = [
             5.3766713954610001e-01,  1.8338850145950865e+00,
            -2.2588468610036481e+00,  8.6217332036812055e-01,
             3.1876523985898081e-01, -1.3076882963052734e+00,
            -4.3359202230568356e-01,  3.4262446653864992e-01,
             3.5783969397257605e+00,  2.7694370298848772e+00,
        ];
        assert::close(&[moment::variance(&data)], &[3.1324921339484746e+00], 1e-15);
    }
}